Deployment of solar photovoltaic (PV) systems is accelerating as the costs of PV panels and other components decrease. Solar PV system installations are further encouraged by various state and federal tax and depreciation credits. To avoid relatively large up-front installation costs, customers deploying a PV system may finance or lease the PV system. To increase the pool of investment capital available for financing or leasing the PV systems, solar leases may be securitized and sold to investors who may be interested in the tax advantages or financial benefits derived from the on-going electrical production provided by the PV systems.
When the electrical production of PV systems is securitized, the value and risk associated with resulting solar backed securities hinges on the accuracy with which the long-term electrical production of the PV systems can be predicted. Predicting the electrical production of PV systems is a complicated task, especially when the electrical production is provided by multiple PV systems at a variety of locations. Variations in the tilt and orientation of the PV panels, or “modules” in the various PV systems, variations in the fraction of direct and diffuse components in the incident solar radiation, spectral effects in the incident solar radiation and the response of the modules in the PV systems to the spectral effects each contribute to irradiance errors. The irradiance errors, when not accounted for, degrade the accuracy of the predicted electrical production of the PV systems. Temperature variations also contribute to errors in the predicted electrical production. The temperature of the cells within the modules depends on multiple factors, such as the ambient air temperature at each PV system, the wind speed, and the incident solar radiation. In addition, the weather data used in predicting electrical production of the PV systems may be provided by weather stations that may be relatively far from the installation sites, which may make it difficult to determine the solar irradiance and the temperature of the cells within the various PV systems.
In addition, there is some fractional loss in electrical production each year due to aging of the modules in the PV systems. Since PV systems may operate for 25 years or more, even very small aging rates (of a fraction of a percent per year) significantly impact the long-term electrical production from the PV systems both in later years, and when viewed cumulatively, over the life of the system. A solar backed security may be sold after approximately 5 years, when depreciation tax credits are exhausted. Because aging effects are typically very small in the first few years of operation of a PV system, it is difficult to accurately determine the aging rate based on this relatively short time period before a PV system may be securitized and sold, especially in view of the other sources of error in predicting electrical production of the PV system stated above. Other impairments, such as soiling and shading of modules, influence the electrical production of the PV systems. Unless accounted for, these impairments may further degrade the accuracy in the predictions of electrical production.
Predicting the electrical production of a PV system is further constrained by significant pressure to reduce costs in PV systems in terms of dollars per Watt of electrical production. Cost pressures may prohibit inclusion of weather monitoring equipment or other monitoring equipment or services that add to the installation costs or operating costs of a PV system. This is especially true of residential PV systems, which are smaller and provide relatively low revenue from electrical production. In residential PV systems, monitoring of electrical production is typically limited to an AC power meter. Hence there is a need for a low-cost method of accurately estimating the long-term PV electrical production.
Known techniques employed in software such as PVWATTS and disclosed by Bill Marion, “Overview of the PV Module Model in PVWatts” [PV Performance Modeling Workshop Albuquerque, N. Mex. Sep. 22, 2010 NREL/PR-520-49607] rely on Typical Meteorological Year (TMY) data to establish solar irradiance, ambient temperature, and wind speed to model the electrical production of a PV system. The model also uses configuration data for a PV system that includes the number of modules, the type of modules, the orientation (tilt and azimuth) of the modules as well as the location of the PV system. Temperature coefficients and other electrical performance parameters used in the model are typically derived from module-specific datasheets. Fixed derating may be relied upon to account for reductions in efficiency of the PV systems due to shading, mismatch of modules, low irradiance illumination production, inverter efficiency, soiling, and aging.
The TMY data provided by a weather station that is nearest to a PV system may still be as far as, for example, 10 km away from the location of the PV system being modeled. The configuration data, typically provided by datasheets, and fixed derating are both approximations to actual performance of the PV system. These factors in sum may provide variability of up to 20% between the predicted AC power output by the PV system and the annual output that is actually measured by an AC power meter [National Renewable Energy Laboratory, http://www.nrel.gov/rredc/pvwatts/interpreting_results.html Nov. 12, 2013].
Some averaging of weather related errors year-to-year may reduce the long-term uncertainty. However, local meteorological conditions not captured by the TMY data are not remedied by averaging. In addition, for a solar backed security that is sold after approximately 5 years, variability in the running average irradiance over 5 years is still approximately 2-3% year-to-year, and the error in the long-term production estimates in PVWATTS using standard derating is closer to 10-12%.
This type of modeling may not predict electrical production of PV systems with the accuracy needed for securitizing electrical production of PV systems. Accordingly, there is a need to predict electrical production with an accuracy that is closer to that of other financial instruments (typically 1% or better). While it may not be possible to achieve this level of accuracy for solar backed securities, improvements in the estimates of electrical production that approach these values may make solar-backed securities attractive to the financial community and may provide the needed capital to increase the pool of investment capital available for financing or leasing the PV systems.